Simplify the following expression and state the condition under which the simplification is valid. You can assume that $t \neq 0$. $n = \dfrac{t}{10(3t - 10)} \div \dfrac{7}{9(3t - 10)} $
Answer: Dividing by an expression is the same as multiplying by its inverse. $n = \dfrac{t}{10(3t - 10)} \times \dfrac{9(3t - 10)}{7} $ When multiplying fractions, we multiply the numerators and the denominators. $n = \dfrac{ t \times 9(3t - 10) } { 10(3t - 10) \times 7 } $ $ n = \dfrac{9t(3t - 10)}{70(3t - 10)} $ We can cancel the $3t - 10$ so long as $3t - 10 \neq 0$ Therefore $t \neq \dfrac{10}{3}$ $n = \dfrac{9t \cancel{(3t - 10})}{70 \cancel{(3t - 10)}} = \dfrac{9t}{70} $